The invention discloses a passive magnetorheological vibration damping device and vibration damping method of a large-sized power generator end winding; the vibration damping device comprises a plurality of passive magnetorheological dampers with the same structures, wherein the passive magnetorheological dampers are arranged on the external wall surface of the power generator end winding; the plurality of passive magnetorheological dampers are uniformly placed on the external wall surface of the motor end winding in a circumferential direction; the other end of each passive magnetorheological damper is fixedly connected with a stand of a power generator by a bracket; and the plurality of passive magnetorheological dampers are used for suppressing vibrations generated by the power generator end winding. Through the adoption of the passive magnetorheological vibration damping device disclosed by the invention, the vibration of the end winding of the large-sized power generator can be effectively suppressed by using an end leakage magnetic field of the power generator end winding; and the passive magnetorheological vibration damping device disclosed by the invention obtains self-adaptivity. The invention further discloses the passive magnetorheological vibration damping method of the large-sized power generator end winding; and through the adoption of the vibration damping device, the method is convenient in operation and the vibration of the end winding of the large-sized power generator can be effectively suppressed.